The present invention relates generally to crosswell seismic imaging and more particularly to a method for producing high vertical resolution tomograms in a crosswell imaging environment by utilizing a node/layer model of a subterranean region of ground.
In fields such as geophysics and geology, the knowledge of the subsurface structure of the ground is useful, for example, in the selection of potential well sites and in fault studies. In the past, a number of different seismic imaging or tomography methods have been implemented with the goal of rendering images which impart such knowledge of the subsurface geologic structure. One such method, which is commonly referred to as crosswell imaging also known as transmission tomography, will be described immediately hereinafter.
Turning immediately to FIG. 1, crosswell imaging is typically performed using a crosswell imaging system which is generally indicated by the reference numeral 10. In system 10, seismic energy 12 is transmitted through a subsurface region 14 of the ground using a source 16 which is positioned in a first borehole 18. In state of the art systems, source 16 typically transmits seismic energy 12 into region 14 in the form of a swept frequency signal (chirp) which covers a predetermined frequency range. Source 16 is selectively movable between a series of positions S.sub.1 through S.sub.N using a winch and cable arrangement 20 wherein source 16 is shown initially at S.sub.1, adjacent the surface of region 14, and is shown in phantom at SN, adjacent the bottom of borehole 18. In order to properly couple source 16 with the subsurface surrounding first borehole 18, source 16 is typically immersed in a liquid or mud (neither of which is shown) which is either present or introduced into borehole 18. It should be noted that the subsurface structure of the ground being imaged is not illustrated in the present figure for purposes of clarity.
Still referring to FIG. 1, seismic energy 12 passes through region 14 and is received by a receiver array 22 which is positioned within a second borehole 24. Like source 16, receiver array 22 is normally immersed in some medium (not shown) for coupling the seismic energy from the ground to the receiver array and, further, is selectively movable between positions R.sub.1 through R.sub.s using a winch and cable arrangement 26 wherein receiver array 22 is initially shown at R.sub.1, adjacent the surface of region 14 and is shown in phantom at R.sub.s, adjacent the bottom of borehole 24. It should be appreciated that the subterranean region of interest may comprise a zone (not shown for purposes of simplicity) which is at a known depth below the surface. In this case, the source and receiver array positions are adjusted accordingly such that the positions are spaced across the zone of interest rather than extending all the way to the surface. Receiver array 22 is made up of any suitable number of receivers such as, for example, five receivers 22a-e to record seismic energy 12 at five vertically spaced positions which are, of course, locationally dependent upon the overall position (one of R.sub.1 through R.sub.s) of the receiver array. It is noted that the first and second boreholes are illustrated as being perfectly vertically oriented for purposes of simplicity. Deviation of these boreholes from the perpendicular direction is typically referred to as well or borehole deviation. Inasmuch as borehole deviation is a concern with regard to portions of the remaining discussions, it will be addressed at appropriate points below.
During the operation of imaging system 10, a series of source scans is performed in each of which source 16 transmits seismic signal 12 in sequence from positions S.sub.1 through SN with receiver array 22 located at one of the positions selected from R.sub.1 through R.sub.S. In one method for completing the source scans, receiver array 22 is initially located at R.sub.1 during a first source scan. This first source scan begins with source 16 transmitting from S.sub.1 such that seismic signal 12 propagates through region 14 and is received at R.sub.1, as illustrated by raypaths 28a-e which are associated with each of receivers 22a-e. Raypaths are commonly used in the art as an expedient in describing the propagation of a wavefront through some medium wherein the raypath representation is perpendicular to the actual wavefront at any particular point therealong. For purposes of simplicity, raypaths illustrated in FIG. 1 are shown as being straight. However, it is recognized that specific subsurface structural features such as, for example, stratifications, often result in raypaths which are not straight and that energy propagated along any of these raypaths, whether straight or curved, is readily detected by receiver array 22. It is further recognized with regard to raypaths that seismic energy propagates along each raypath, as defined between source 16 and a respective receiver (one of 23a-e), at some average velocity which is dependent upon the structural features and velocity characteristics of the materials that are encountered along the overall length of the raypath. This average velocity is normally considered in terms of a "traveltime" which is associated with each raypath. Traveltimes are categorized in terms of particular characteristics of their associated seismic wave types. In the particular instance of seismic waves that travel from source to receiver without being reflected or converted to another wave type, traveltimes are referred to as direct arrival as contrasted with, for example, reflected (non-direct) arrival. One of skill in the art will recognize that direct and reflected arrival traveltimes may be individually separated from the overall seismic data record using known techniques.
Continuing to refer to FIG. 1 and as the scanning operation continues, source 16 is moved/scanned in the direction indicated by an arrow 27 to successive source positions up to and including S.sub.N such that data is recorded for each of positions S.sub.1 through S.sub.N with the receiver array located at R.sub.1. Next, receiver array 22 is moved in the direction indicated by an arrow 29 to position R.sub.2 (not shown) and source 16 is returned to position S.sub.1 at which time the source scan is repeated in the aforedescribed manner wherein seismic signal 12 is transmitted from each of positions S.sub.1 through S.sub.N so as to complete a second source scan corresponding to receiver position R.sub.2. The inception of the final source scan (performed with receiver array 22, shown in phantom, at Rs) is illustrated wherein source 16 initially transmits from S.sub.1 to R.sub.S. When compared with the S.sub.1 -R.sub.1 transmission, it is noted that the S.sub.1 -R.sub.S transmission produces raypaths 30a-e which, relative to the other raypaths, most closely approach a vertical direction through region 14. The significance of such "more vertically oriented" raypaths will be described in detail at an appropriate point below in conjunction with a discussion of characteristics of the seismic data record which are recognized by the present invention. For the moment, however, it is sufficient to note that the maximum vertical orientation of raypaths within region 14 is directly related to an aperture angle .alpha. which is defined, as illustrated, by the depth d of boreholes 18 and 24 in conjunction with a distance w by which the boreholes are separated. A final source scan is completed with the source/receiver positions Sn-Rn. It is noted that this operation may be performed in any number of different ways so long as measurements are obtained between each receiver position (within the overall receiver array) and each source position so as to produce a seismic data record which is representative of region 14.
The seismic data record, in and by itself, represents a relatively complex, rather large body of information. For example, a typical seismic data record may be obtained using two hundred different source transmission positions (S.sub.1 through S.sub.N, above) in combination with two hundred different receiver positions (i.e., forty different positions of receiver array 22) yielding forty thousand possible straight raypaths through the region of interest. Crosswell imaging contemplates the use of this data in a way which produces a seismic velocity map that is intended to represent the subsurface structure within the region of interest based on the principle that different material layer types exhibit different seismic velocities. More specifically, by measuring the time of arrival of the seismic energy along any given path (direct or indirect) and knowing the path length, the average velocity traveled by the seismic energy along its path can be determined. However, the usefulness of any particular velocity map is related to its resolution and accuracy. Moreover, any velocity map should preferably be readily correlated with other forms of seismic records which are in popular use such as, for example, sonic well logs. In the past, various approaches have been taken for using the seismic data record in attempting to produce such images. In each of these approaches, the region of interest must be mathematically modeled in such a way that the seismic data record may be applied to the model. Thus, the model, at least initially, forms the basis for the image which is produced by a respective approach to the problem.
Still referring to FIG. 1 and in one particular modeling approach, region 14 is divided into relatively small areas which are referred to as pixels 32. For purposes of clarity, only pixels within one portion of region 14 are illustrated. However, it is to be understood that pixels 32 cover the entirety of the region. Typically, each pixel 32 is square in form and is assumed to be homogeneous with regard to its seismic properties such as wave propagation velocity. Thus an equation may be expressed for any raypath through region 14 in the form: EQU t=d.sub.1 /v.sub.1 +d.sub.2 /v.sub.2 +. . . +d.sub.n /v.sub.n(1)
wherein t is the known direct arrival traveltime for a particular raypath which is obtained directly from the seismic data record, n represents the number of pixels which the raypath transverses, d.sub.1 through d.sub.n represent the incremental distances across the individual pixels along the raypath and v.sub.1 through v.sub.n represent the corresponding seismic velocity within each pixel along the ray path. It should be appreciated that the d.sub.1 through d.sub.n numerator values may readily be obtained since the pixel locations are known and since, for an assumed straight raypath between particular source and receiver positions, the endpoints of the raypath are known. However, it is appropriate to now mention that well deviation should be considered in determining raypath lengths, which influences t, so as to ensure accuracy of the formulated equation. Further discussion will be directed to the subject of well deviation where appropriate.
As a particular example of the development of a raypath equation, a raypath 34 is shown which extends from an exemplary source position S.sub.150 directly to receiver 23e with receiver array 22 located at position R.sub.1 such that distances d are defined within pixels 36 (d1), 38 (d2), 40 (d3), 42 (d4), 44 (d5), 46 (d6), etc. As noted values are readily obtained and the associated traveltime t is known leaving only v.sub.1 through V.sub.n as unknown values within equation 1. In this manner, a system of equations, each of which is in the form of equation 1, may be set up based on any number of known direct arrival traveltimes and associated raypaths. The system may then be solved to yield the pixel velocity values using known mathematical techniques. Using the pixel velocity values, a velocity map may then be produced. On the assumption that the obtained velocity values for this pixelated model are accurate, the geologist or geophysicist is presented with a powerful tool.
For reasons which will become evident, however, it is submitted that the pixelated model has not met the goal of providing high resolution accurate imaging. It is noted that, even though the aforedescribed procedure used in developing a pixel type velocity map, represents a somewhat simplified version of the actual procedure which is used in producing an initial velocity map, this description serves to clearly illustrate the reason for its particular weakness. More specifically, each pixel within region 14 represents an unknown velocity value. As described above, a typical seismic data record may contain, for example, approximately forty thousand direct arrival traveltimes. Unfortunately, a particular pixelated model may contain such a large number of pixels that the known direct arrival traveltimes are far outnumbered. Such a model results in an under determined system of equations for which more than one correct velocity solution exists yielding a relatively low resolution (inaccurate) image as compared, for example, with typical well log records.
Various techniques have been applied in an attempt to deal with this ambiguity of solutions and thereby improve resolution. For example, limitations have been placed on velocity values assigned to adjacent pixels. As another example, larger pixels have been used. These techniques, thus far, have yielded insufficient resolution improvements, producing tomograms which are considered to be of limited value by those of skill in the art. In fact, it is now believed by many of skill in the art that high resolution seismic tomography is an impractical expectation.
As a consequence, still further techniques have been developed in attempting to cope directly with the low resolution problem. For instance, the distribution of pixels has been changed such that areas of particular interest within a region are covered by a greater number of pixels than those areas which are not considered to be of interest. However, the goal of high resolution seismic tomography remains unattained using this technique, and other similar techniques, for reasons which are recognized by the present invention and which will be described hereinafter.
It is noted that models other than the pixelated type have been developed for use in describing subsurface structure. One such model was described by Harris (1994) in his paper entitled, "An approach to adaptive gridding for traveltime tomography" and employs a distribution of nodes throughout the region of interest. The subject paper introduces the concept of nodes, but offers no guidelines or "rules" as to how to place the nodes in order to extract optimum resolution.
The present invention solves the high resolution seismic tomography problem by using a highly advantageous model and associated method which have not been seen heretofore and which have been developed in recognition of the unique nature of seismic data records. Additionally, the present invention provides a heretofore unseen, simple and highly effective technique which compensates for borehole deviation.